17 citations · 162 across the 31 of their papers we have counts for
8 papers · 1 filter
The planar -colorable subgroup of Thompson's group and its even part
Valeriano Aiello, Tatiana Nagnibeda
We study the planar -colorable subgroup of Thompson's group and its even part . The latter is obtained by cutting with a…
On the -colorable subgroup and maximal subgroups of Thompson's group
Valeriano Aiello, Tatiana Nagnibeda
In his work on representations of Thompson's group , Vaughan Jones defined and studied the -\emph{colorable subgroup} of . Later, Ren showed that it is isomo…
On the oriented Thompson subgroup and its relatives in higher Brown-Thompson groups
Valeriano Aiello, Tatiana Nagnibeda
A few years ago the so-called oriented subgroup of the Thompson group was introduced by V. Jones while investigating the connections between subfactors and conformal f…
On spectral measures for certain unitary representations of R. Thompson's group F
Valeriano Aiello, Vaughan F. R. Jones
The Hilbert space of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group via local scale transformations…
Jones representations of Thompson's group arising from Temperley-Lieb-Jones algebras
Valeriano Aiello, Arnaud Brothier, Roberto Conti
Following a procedure due to V. Jones, using suitably normalized elements in a Temperley-Lieb-Jones (planar) algebra we introduce a 3-parametric family of unitary representations o…
The Homflypt polynomial and the oriented Thompson group
Valeriano Aiello, Roberto Conti, Vaughan F. R. Jones
We show how to construct unitary representations of the oriented Thompson group from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT…
The Jones polynomial and functions of positive type on the oriented Jones-Thompson groups and
Valeriano Aiello, Roberto Conti
The pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups and $\v…
Graph polynomials and link invariants as positive type functions on Thompson's group F
Valeriano Aiello, Roberto Conti
In a recent paper Jones introduced a correspondence between elements of the Thompson group and certain graphs/links. It follows from his work that several polynomial invariants…